The necessity of entanglement and the equivalency of Bell's theorem with the second law of thermodynamics

We demonstrate that both Wigner's form of Bell's inequalities as well as a form of the second law of thermodynamics, as manifest in Caratheáodory's principle, can be derived from the same simple experimental and statistical mechanical assumptions combinedwith the trivial behavior of integers. This suggests that Bell's theorem is merely a well-disguised statement of the second law. It also suggests that entanglement is necessary for quantum theory to be in full accord with the second law and thus builds on the results of Wiesniak, Vedral, and Brukner [1] who showed it was necessary for consistency with the third law.